The Borel character

Frédéric Déglise (1) , Jean Fasel (2)

1 IMB - Institut de Mathématiques de Bourgogne [Dijon]
2 IF - Institut Fourier

The main purpose of this article is to define a quadratic analogue of the Chern character, the so-called Borel character, that identifies rational higher Grothendieck-Witt groups with a sum of rational Milnor-Witt (MW)-motivic cohomologies and rational motivic cohomologies. We also discuss the notion of ternary laws due to Walter, a quadratic analogue of formal group laws, and compute what we call the additive ternary laws, associated with MW-motivic cohomology. Finally, we provide an application of the Borel character by showing that the Milnor-Witt K -theory of a field F embeds into suitable higher Grothendieck-Witt groups of F modulo explicit torsion.

Mots clés: motivic homotopy; hermitain K-theory; MW-motivic cohomology; characteristic classes

Domaines: Géométrie algébrique [math.AG]; K-théorie et homologie [math.KT]

Frédéric Déglise, Jean Fasel. The Borel character. Journal of the Institute of Mathematics of Jussieu, 2021, pp.1-51. ⟨10.1017/S1474748021000281⟩. ⟨ensl-03466895⟩